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<b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="valued_2.html#K10" title="VALUED_2:func.10">I_Funcs</a> <font color="Maroon" title="c2">X</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="valued_2.html#K9" title="VALUED_2:func.9">I_PFuncs</a> <font color="Maroon" title="c2">X</font></span>)</span></span><br/>

<a NAME="E1:35"/>
 <a href="valued_2.html#K10" title="VALUED_2:func.10">I_Funcs</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="valued_2.html#K9" title="VALUED_2:func.9">I_PFuncs</a> <font color="Maroon" title="c2">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="valued_2.html#K10" title="VALUED_2:func.10">I_Funcs</a> <font color="Maroon" title="c2">X</font> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="valued_2.html#K9" title="VALUED_2:func.9">I_PFuncs</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<b>assume </b><a NAME="E1:35_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="valued_2.html#K10" title="VALUED_2:func.10">I_Funcs</a> <font color="Maroon" title="c2">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="valued_2.html#K9" title="VALUED_2:func.9">I_PFuncs</a> <font color="Maroon" title="c2">X</font></span><br/>

<a NAME="E2:35_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">X</font>, <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<b>by </b><i><a class="ref" href="valued_2.html#D16" target="_self" title="VALUED_2:def.16">Def16</a></i>;<br/>
<b>hence </b><a NAME="E3:35_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="valued_2.html#K9" title="VALUED_2:func.9">I_PFuncs</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="ref" href="valued_2.html#D15" target="_self" title="VALUED_2:def.15">Def15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:35"/>
 <a href="valued_2.html#K10" title="VALUED_2:func.10">I_Funcs</a> <font color="Maroon" title="c2">X</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="valued_2.html#K9" title="VALUED_2:func.9">I_PFuncs</a> <font color="Maroon" title="c2">X</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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